TIPS Ladder Spreadsheets in General & Two in Particular

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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by #Cruncher »

Kevin M wrote: Sat Jan 27, 2024 11:46 amSay I want to get about the same real income in Jan and Jul of a year. If I enter 0.5 for each into the multiplier column, the quantity Needed and Principal are much larger for Jan than for Jul.
I've modified the "Ladder" sheet of the workbook to solve this. When more than one TIPS is chosen for a single maturity year, the interest on TIPS maturing in later years is split amongst them in proportion to their "Multiplier" values.
Mezzinmi wrote: Tue Jan 30, 2024 9:56 amIt looks like you can enter the same date for settlement and base dates and same ref CPI for that date. (The date of the WSJ quotes?)
"Settlement date of WSJ Quotes" and "Ref CPI on Settlement Date" (cells K1 and K2 on the "Ladder" sheet) are used to compute the cost including accrued interest. By default I set the "Real $ Base Date" and "Ref CPI on Base Date" (cells G1 and G2) to the same values. But if you're buying a ladder in stages, you may want to keep the base values constant to maintain consistent principal values of TIPS bought at different times. (But be aware that the annual returns on the "XIRR" row of the "XIRR" cash flow sheet are only accurate when the Ref CPI values in cells G2 and K2 are the same.)
Mezzinmi, in same post, wrote:What is your criteria for selecting the specific TIPS ... in your spreadsheet? In the tipsladder.com tool, I think you can choose among best yield, earliest/latest maturity, etc.
I ignore yield in picking the one default TIPS for each year that more than one matures. I do consider the following:
  • Pick most recently issued hoping that it will be most liquid. E.g., pick 5-year over 10-year and 10-year over 20-year.
  • Try to maintain close to 12-month spacing.
  • Pick the latest maturity before the gap running to 2039.
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Kevin M
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

#Cruncher wrote: Fri Feb 02, 2024 5:21 pm
Kevin M wrote: Sat Jan 27, 2024 11:46 amSay I want to get about the same real income in Jan and Jul of a year. If I enter 0.5 for each into the multiplier column, the quantity Needed and Principal are much larger for Jan than for Jul.
I've modified the "Ladder" sheet of the workbook to solve this. When more than one TIPS is chosen for a single maturity year, the interest on TIPS maturing in later years is split amongst them in proportion to their "Multiplier" values.
OK, the ladder sheet seems to work correctly now with more than one TIPS per year (thanks!), but the XIRR sheet does not; I now see that it wasn't working in the last rev either. It assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all.

I own TIPS in each maturity month for the earlier years, and I plan to do something similar for all years, so I have 37 different TIPS in the ladder sheet going out to 2047 (23 years). For $50K/year, cost is 923,762. The XIRR sheets shows cost of 638,138, and only includes TIPS through 2040.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by #Cruncher »

Kevin M wrote: Sat Feb 03, 2024 1:49 pm... the XIRR sheet ... assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all. ... I have 37 different TIPS in the ladder sheet ...
I've expanded the workbook's XIRR and ToPaste sheets to handle up to 50 selected TIPS.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Prudence »

For my first time, I used the Ladder Builder spreadsheet to build a TIPS ladder from 2025 to 2044. Suppose I wish to invest my entire IRA in TIPS. If I choose a $50,000 DARA (Desired Annual Real Amount), the total cost of the ladder will be about 90% of my IRA current balance (for 2025 through 2044).
Questions:
1. If I wish to invest the remaining 10% in my IRA in the TIPS ladder, should I increase the DARA (>$50,000), or, extend the ladder beyond 2044?
2. If DW and I die before the end of the ladder, can our heirs keep the TIPS until the maturity dates, if they choose?
3. Our accounts are at Vanguard. If desired, to satisfy future RMDs, is it possible to do an in-kind transfer of individual TIPS bonds from the IRA to our taxable account?
4. To deal with the "gap" (2035 to 2039), is there a BH preferred approach? Options include: three years in 2034 maturity and four years in 2040; or put seven years in 2034 maturity; or double up on maturity years 2025 through 2029 with intent to roll over half on maturity each year to fill the 2035 through 2039 gap years?
5. Suppose I wish to use my DW's IRA to fill the rungs in the TIPS ladder. So, 100% of the balances in our IRAs would be invested in TIPS. Do I need to build two separate ladders using the Ladder Builder spreadsheet?
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

Prudence wrote: Sun Feb 04, 2024 4:20 pm For my first time, I used the Ladder Builder spreadsheet to build a TIPS ladder from 2025 to 2044. Suppose I wish to invest my entire IRA in TIPS. If I choose a $50,000 DARA (Desired Annual Real Amount), the total cost of the ladder will be about 90% of my IRA current balance (for 2025 through 2044).
Questions:
1. If I wish to invest the remaining 10% in my IRA in the TIPS ladder, should I increase the DARA (>$50,000), or, extend the ladder beyond 2044?
2. If DW and I die before the end of the ladder, can our heirs keep the TIPS until the maturity dates, if they choose?
3. Our accounts are at Vanguard. If desired, to satisfy future RMDs, is it possible to do an in-kind transfer of individual TIPS bonds from the IRA to our taxable account?
4. To deal with the "gap" (2035 to 2039), is there a BH preferred approach? Options include: three years in 2034 maturity and four years in 2040; or put seven years in 2034 maturity; or double up on maturity years 2025 through 2029 with intent to roll over half on maturity each year to fill the 2035 through 2039 gap years?
5. Suppose I wish to use my DW's IRA to fill the rungs in the TIPS ladder. So, 100% of the balances in our IRAs would be invested in TIPS. Do I need to build two separate ladders using the Ladder Builder spreadsheet?
1. Either one is fine. If you've based your DARA on your necessary residual living expenses, then extending the ladder provides more longevity insurance, while increasing the DARA allows you to spend more than what you think you'll need to. Another way to look at it is that increasing your DARA increases your reinvestment risk, since you might roll excess proceeds of maturing TIPS into longer maturity TIPS at unknown future prices, while adding rungs increases your price risk, since you might want to sell those before maturity at unknown prices to spend more in earlier years.

2. Yes. Typically the assets would be transferred into the inherited IRAs of the heirs, who can then do what they want with them. They'll need to take their RMDs, but they should be able to do that by taking in-kind distributions of the TIPS. See #3.

3. Yes, based on other posts I've seen you can do this, but it's easy enough to call Vanguard and ask, or search their website for the answer. Maybe someone who's actually done this can chime in. But since you'll have rungs maturing each year, why not just take the distribution from the proceeds of the matured TIPS?

4. Any of the options you listed are acceptable. My thinking is that I want something with a similar duration to the gap maturities, so as prices and yields change, the ones I own will change most like the ones I want to buy later would change if they existed. The 2034 is closest to the 2035 and 2036, the 2040 is closest to the 2038 and 39, and the 2037 is right in the middle. So I entered 3.5 as the multiplier for the 2034 and 2040, planning to use 2.5X of each to cover the five gap years. So next year I could sell some 2034s to buy some 2035s, or if I really wanted to maintain the duration of the gap years, I could sell mostly 2034s but some 2040s.

5. You can do it with one ladder or two, whichever suits your preference. If you like to view your joint assets as one portfolio, then one ladder might make more sense. Simply increase the DARA and/or add rungs until the ladder cost is about the amount in both IRAs. If you have a reason to account for them separately, then you could build two ladders.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

#Cruncher wrote: Sun Feb 04, 2024 4:14 pm
Kevin M wrote: Sat Feb 03, 2024 1:49 pm... the XIRR sheet ... assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all. ... I have 37 different TIPS in the ladder sheet ...
I've expanded the workbook's XIRR and ToPaste sheets to handle up to 50 selected TIPS.
Looks good! Thanks.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Prudence »

Thanks again, Kevin, for the perfect reply. And thank you #Cruncher (and your collaborators) for the essential ladder builder.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by protagonist »

Kevin M wrote: Sun Feb 04, 2024 5:48 pm

4. Any of the options you listed are acceptable. My thinking is that I want something with a similar duration to the gap maturities, so as prices and yields change, the ones I own will change most like the ones I want to buy later would change if they existed. The 2034 is closest to the 2035 and 2036, the 2040 is closest to the 2038 and 39, and the 2037 is right in the middle. So I entered 3.5 as the multiplier for the 2034 and 2040, planning to use 2.5X of each to cover the five gap years. So next year I could sell some 2034s to buy some 2035s, or if I really wanted to maintain the duration of the gap years, I could sell mostly 2034s but some 2040s.


I have another thought about this, though it may not pertain to everybody....

Every year I will be receiving a certain amount of income, between maturing TIPS, SS , and capital gains distributions/dividends, above what I will probably spend. Unless TIPS no longer become a worthwhile fixed income investment (which, to me, means essentially a positive YTM), I would probably invest that money in TIPS, extending my ladder. I don't currently have much free cash to invest.

Right now my ladder is pretty equally invested in years from 2024-2034 with a few 204xs.

If I sold TIPS from my ladder now to over-invest in 2034s and 2040s to lock in today's rates, I would still be in a position of having to decide what to do with the excess income every subsequent year, and if I put it in TIPS I would still be subject to market rates at the time of investment.

So I am not sure if selling TIPS now to over-fund 2034 and 2040 (vs, just buying 2035-39s with cash when those become available) would really help me much. Plus, it would tie up money for a longer period (I will be 88 in 2040).

Thoughts?
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Wrench »

protagonist wrote: Sun Feb 04, 2024 7:18 pm

So I am not sure if selling TIPS now to over-fund 2034 and 2040 (vs, just buying 2035-39s with cash when those become available) would really help me much. Plus, it would tie up money for a longer period (I will be 88 in 2040).

Thoughts?
If I were you, I would wait and buy to fill the gap in the future with accrued cash. In general, I try not to rearrange assets just because there is a "good deal" on something else. Also, it's now only 11 months until 2035 TIPS will be available. No one knows, but it seem likely to me that YTM on that issue will at least be positive, meeting your criteria for buying. Also, you will be a year older and have one more year of knowledge about your health, the state of the economy, and life in general. Each year, you can make the choice - buy one more year, or fill the gap completely. Who knows, maybe in a year or two stocks will be a screaming buy, and buying TIPS will look silly. Really though, either path works. You just need to be comfortable with what you choose.

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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by protagonist »

Thanks, Wrench.

That is sort of my thinking....it's just that so many people here advocate the "overbuying 2034/204x" approach that I have had second thoughts. I see its merits.
I started building my ladder in mid-2022 when the discussion of this sort of thing was still pretty embryonic.

My main reason for leaving well enough alone is inertia.

But I am interested in others' thoughts.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Prudence »

Kevin M wrote: Sun Feb 04, 2024 5:58 pm
#Cruncher wrote: Sun Feb 04, 2024 4:14 pm
Kevin M wrote: Sat Feb 03, 2024 1:49 pm... the XIRR sheet ... assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all. ... I have 37 different TIPS in the ladder sheet ...
I've expanded the workbook's XIRR and ToPaste sheets to handle up to 50 selected TIPS.
Looks good! Thanks.
I am thinking of using a TIPS Ladder and the Vanguard intermediate TIPS fund for my IRA (because my annual residual expenses are difficult to predict). If the VG fund has a 6.5 average years duration, to partially mitigate interest rate risk, what if I build a ladder to cover 6.5 years (2024 through 2030) and invest the rest of the IRA in the fund? (The goal remains to invest 100% of the IRA in TIPS). It is no bother for me to manage. What you think of this approach?
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

protagonist wrote: Sun Feb 04, 2024 7:18 pm
Kevin M wrote: Sun Feb 04, 2024 5:48 pm 4. Any of the options you listed are acceptable. My thinking is that I want something with a similar duration to the gap maturities, so as prices and yields change, the ones I own will change most like the ones I want to buy later would change if they existed. The 2034 is closest to the 2035 and 2036, the 2040 is closest to the 2038 and 39, and the 2037 is right in the middle. So I entered 3.5 as the multiplier for the 2034 and 2040, planning to use 2.5X of each to cover the five gap years. So next year I could sell some 2034s to buy some 2035s, or if I really wanted to maintain the duration of the gap years, I could sell mostly 2034s but some 2040s.
I have another thought about this, though it may not pertain to everybody....

Every year I will be receiving a certain amount of income, between maturing TIPS, SS , and capital gains distributions/dividends, above what I will probably spend. Unless TIPS no longer become a worthwhile fixed income investment (which, to me, means essentially a positive YTM), I would probably invest that money in TIPS, extending my ladder. I don't currently have much free cash to invest.

Right now my ladder is pretty equally invested in years from 2024-2034 with a few 204xs.

If I sold TIPS from my ladder now to over-invest in 2034s and 2040s to lock in today's rates, I would still be in a position of having to decide what to do with the excess income every subsequent year, and if I put it in TIPS I would still be subject to market rates at the time of investment.

So I am not sure if selling TIPS now to over-fund 2034 and 2040 (vs, just buying 2035-39s with cash when those become available) would really help me much. Plus, it would tie up money for a longer period (I will be 88 in 2040).

Thoughts?
Overloading the 2034s and/or 2040s reduces risk. When the Jan 2035 is issued, the yield is likely to be in the ball park of the 2034, so buying extra 2034s now is as close as we can get to locking in the 2035 yield.

I believe you're a proponent of buying if we're happy with the yields, even if they aren't 2% or more (the McQ idea of buying when the real yield is as high as the long-term real return of government bonds). The 2034 now is about 1.9% (now 1.87%, down from 1.9% when I first looked earlier today). It was auctioned at 1.81%.

I too will have boatloads of proceeds from coupons and maturing TIPS over the next few years, since I loaded up on TIPS with maturities of less than five years. That essentially is part of my risk portfolio. I can use the proceeds to surf the TIPS yield curve, or I might decide to buy nominal bonds or even stocks.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by sycamore »

Prudence wrote: Mon Feb 05, 2024 11:51 am
Kevin M wrote: Sun Feb 04, 2024 5:58 pm
#Cruncher wrote: Sun Feb 04, 2024 4:14 pm
Kevin M wrote: Sat Feb 03, 2024 1:49 pm... the XIRR sheet ... assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all. ... I have 37 different TIPS in the ladder sheet ...
I've expanded the workbook's XIRR and ToPaste sheets to handle up to 50 selected TIPS.
Looks good! Thanks.
I am thinking of using a TIPS Ladder and the Vanguard intermediate TIPS fund for my IRA (because my annual residual expenses are difficult to predict). If the VG fund has a 6.5 average years duration, to partially mitigate interest rate risk, what if I build a ladder to cover 6.5 years (2024 through 2030) and invest the rest of the IRA in the fund? (The goal remains to invest 100% of the IRA in TIPS). It is no bother for me to manage. What you think of this approach?
Let's imagine you go ahead and buy a 6.5 year ladder and invest the rest in a TIPS fund.

From the get-go the average duration of your combined ladder+fund is slightly less than the 6.5 duration of the fund, make sense? Maybe 5 years or so, depends on how much is in the ladder or fund, but you get the idea.

After 1 year, the first rung of the ladder matures and you presumably spend the proceeds. Now the average duration of your combined ladder+fund is a bit longer than when you started. Maybe up to 5.25.

After another year you spend the proceeds from another maturing rung. Now your average duration is up to 5.5.

And so on until the last run matures. And you're left with the fund and its 6.5 year duration.

All along you'll get the coupon payments (from bonds) and dividends (from the fund).

That's what will happen, roughly speaking. Is that what you want or expect?


With the ladder I think you basically bought yourself some certainty about spending for the first 6.5 years. But after that you're back to some uncertainty with the fund as well its price volatility.

Would that be "bad"? Not necessarily, if you understand the nature of how bonds and bond funds work.

Does it mean you shouldn't use a combined ladder and fund? No.

What's your goal with a combination of ladder+fund? Do you think the behavior described above would achieve that goal?

Personally I think that a full-blown non-rolling TIPS-only ladder or an intermediate-term TIPS fund (or somewhere in-between) is entirely reasonable for many investors. I think the differences are less important than the attributes they shares.

With no specifics of your personal situation (like your goals, risk tolerance, and how much will Social Security benefits cover your spending needs?) you'll be stuck with generic answers. Consider starting a new post in the Personal Investments subforum.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

Prudence wrote: Mon Feb 05, 2024 11:51 am I am thinking of using a TIPS Ladder and the Vanguard intermediate TIPS fund for my IRA (because my annual residual expenses are difficult to predict). If the VG fund has a 6.5 average years duration, to partially mitigate interest rate risk, what if I build a ladder to cover 6.5 years (2024 through 2030) and invest the rest of the IRA in the fund? (The goal remains to invest 100% of the IRA in TIPS). It is no bother for me to manage. What you think of this approach?
It's hard for me to see much sense in this. Here are the fund holdings as of 12/31/2023:

Image

(The fund holds some non-TIPS Treasuries--don't know why, but no TIPS mature on any date other than the 15th of the month, so the ones you see with maturity dates like 02/28/30, for example, are not TIPS.)

The fund doesn't hold any TIPS maturing in 2024, but other than that, you'd just be adding to the maturities through 2030.

When your 2025 TIPS mature, I assume you'd spend much if not all of the proceeds. When the fund's 2025 TIPS mature, they'll reinvest the proceeds in longer maturities. Your average duration would gradually increase, while with just a ladder it would gradually decrease.

You could just build a ladder that looks something like the fund, using the same amount of money that you'd put into your ladder plus the fund. Or just build a ladder with even rungs using that amount of money, with the maximum maturity based on your life expectancy. That will provide you with the maximum annual cash flow that you can afford, assuming that you'd put whatever you can afford into the ladder + fund.

If you don't need all of the cash in the year of maturity, you can reinvest it in your TIPS ladder in whatever way makes sense at the time; i.e., either spread it across maturities, put more in earlier maturities, etc. This would be kind of like spending from your partial ladder and having the fund roll the shorter-term TIPS they hit the 1-year mark, but you have the choice to do this or not. If you need more cash in a particular year, sell some other TIPS before maturity; I don't see this as being any worse than selling shares of the fund--maybe better, since you can select particular maturities to sell based on prices and yields.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Prudence »

Awesome, thanks again, Kevin.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Prudence »

sycamore wrote: Mon Feb 05, 2024 6:02 pm
Prudence wrote: Mon Feb 05, 2024 11:51 am
Kevin M wrote: Sun Feb 04, 2024 5:58 pm
#Cruncher wrote: Sun Feb 04, 2024 4:14 pm
Kevin M wrote: Sat Feb 03, 2024 1:49 pm... the XIRR sheet ... assumes a maximum of 30 TIPS, so if you have more than that, it doesn't include them all. ... I have 37 different TIPS in the ladder sheet ...
I've expanded the workbook's XIRR and ToPaste sheets to handle up to 50 selected TIPS.
Looks good! Thanks.
I am thinking of using a TIPS Ladder and the Vanguard intermediate TIPS fund for my IRA (because my annual residual expenses are difficult to predict). If the VG fund has a 6.5 average years duration, to partially mitigate interest rate risk, what if I build a ladder to cover 6.5 years (2024 through 2030) and invest the rest of the IRA in the fund? (The goal remains to invest 100% of the IRA in TIPS). It is no bother for me to manage. What you think of this approach?
Let's imagine you go ahead and buy a 6.5 year ladder and invest the rest in a TIPS fund.

From the get-go the average duration of your combined ladder+fund is slightly less than the 6.5 duration of the fund, make sense? Maybe 5 years or so, depends on how much is in the ladder or fund, but you get the idea.

After 1 year, the first rung of the ladder matures and you presumably spend the proceeds. Now the average duration of your combined ladder+fund is a bit longer than when you started. Maybe up to 5.25.

After another year you spend the proceeds from another maturing rung. Now your average duration is up to 5.5.

And so on until the last run matures. And you're left with the fund and its 6.5 year duration.

All along you'll get the coupon payments (from bonds) and dividends (from the fund).

That's what will happen, roughly speaking. Is that what you want or expect?


With the ladder I think you basically bought yourself some certainty about spending for the first 6.5 years. But after that you're back to some uncertainty with the fund as well its price volatility.

Would that be "bad"? Not necessarily, if you understand the nature of how bonds and bond funds work.

Does it mean you shouldn't use a combined ladder and fund? No.

What's your goal with a combination of ladder+fund? Do you think the behavior described above would achieve that goal?

Personally I think that a full-blown non-rolling TIPS-only ladder or an intermediate-term TIPS fund (or somewhere in-between) is entirely reasonable for many investors. I think the differences are less important than the attributes they shares.

With no specifics of your personal situation (like your goals, risk tolerance, and how much will Social Security benefits cover your spending needs?) you'll be stuck with generic answers. Consider starting a new post in the Personal Investments subforum.
My goals are to invest all of our (me and DW) IRAs in TIPS and that will be our total investment in fixed. I wish to have our fixed portfolio keep pace with inflation and produce a little income. I wish to avoid interest rate risk and I am ok with taking reinvestment risk. After thinking about your post and Kevin M's post, I can see that either a ladder or a fund makes sense, and the ladder is probably the better option for me.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

I had a need to enter different DARAs for each year, so #Cruncher provided a couple of ways to do that. If anyone is interested in why I wanted to do this, and how it can be implemented, I'm sharing it in this thread: Building a TIPS ladder for IRA RMDs - Bogleheads.org.

Bottom line is that the easiest way to do it is to enter $1 in the DARA cell, B2, and enter the individual DARAs in the multiplier column.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

I have a question about both tools. Why does each one use a combination of 2034s and 2040s to cover the gap years? The #Cruncher spreadsheet uses multipliers of 3 and 4 respectively for these bracket years, and tipsladder.com uses different combinations of them depending on the options chosen for "Which TIPS to use to fund a year without a maturing TIPS:".

I've always assumed that this just made sense based on some sort of duration matching scheme, but in my thread, Filling the TIPS gap years with bracket year duration matching - Bogleheads.org, we've discovered that duration matching doesn't really work because the gap year TIPS price will always be close to 100. Duration matching requires that the price of the the TIPS between the bracket years varies with yields, as do the prices of the bracket year TIPS, and this assumption doesn't apply for new issues at auction.

I guess I could see some sense in this if the yield curve had the normal, positively-sloped shape, especially if it was fairly steep, since we'd be taking advantage of higher yields at longer maturities. However, with the currently inverted yield curve, we get higher yields at shorter maturities.

After thinking about it, it seems that currently we could more effectively cover the 2035 gap year with a Jan 2025 TIPS, for example, since there is more certainty of the nominal return when the 2035 is issued in Jan 2025, and the yield is much higher than the 2034 or 2040 TIPS.

:?
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

Kevin M wrote: Tue May 28, 2024 11:03 am I have a question about both tools. Why does each one use a combination of 2034s and 2040s to cover the gap years? The #Cruncher spreadsheet uses multipliers of 3 and 4 respectively for these bracket years, and tipsladder.com uses different combinations of them depending on the options chosen for "Which TIPS to use to fund a year without a maturing TIPS:".

I've always assumed that this just made sense based on some sort of duration matching scheme, but in my thread, Filling the TIPS gap years with bracket year duration matching - Bogleheads.org, we've discovered that duration matching doesn't really work because the gap year TIPS price will always be close to 100. Duration matching requires that the price of the the TIPS between the bracket years varies with yields, as do the prices of the bracket year TIPS, and this assumption doesn't apply for new issues at auction.

I guess I could see some sense in this if the yield curve had the normal, positively-sloped shape, especially if it was fairly steep, since we'd be taking advantage of higher yields at longer maturities. However, with the currently inverted yield curve, we get higher yields at shorter maturities.

After thinking about it, it seems that currently we could more effectively cover the 2035 gap year with a Jan 2025 TIPS, for example, since there is more certainty of the nominal return when the 2035 is issued in Jan 2025, and the yield is much higher than the 2034 or 2040 TIPS.

:?
All quiet on the TIPS tool builders' front.

I feel like we've made progress in the thread linked above. To summarize, I'm coming around to the view that duration matching based on the assumption that the hypothetical gap year TIPS trade on the secondary market is valid, even though the assumption that coupon is fixed, and so is an independent variable and price is the dependent variable in the PV equation for bond price/value, doesn't match reality. Here's my quick summary of my most recent work:
  1. The PV equation for bond value can be rearranged so that coupon is the dependent variable, and price is an independent variable.
  2. Solving this equation results in coupon = yield, which is closer to the reality of a Treasury auction.
  3. This gives me a warm, fuzzy feeling that the same financial benefit is derived from a change in coupon from what it would be now to what it actually is at auction is the same as that derived from a change in yield from what it is now to what it is at auction.
  4. However, I haven't taken the next step, which I think is to show that by duration matching the bracket year TIPS (e.g., 2034 and 2040) to a gap year TIPS, e.g., 2035, one or more swaps (selling ladder TIPS to buy auction TIPS) can be done such that annual real income (ARA) remains close to DARA for each issue held in the ladder.
  5. As implied in #4, I've zeroed in on ARA = DARA after the gap year swap(s) as the primary goal of optimizing a duration matching strategy.
I've had difficulty trying to simulate this with the #Cruncher spreadsheet, due to the special handling of the 2034 to cover the gap years--at least it seems that way to me. The last bit of work I did on this was to work with a 10-year ladder, and treat one of the earlier years as a gap year, say gap - 2032, with bracket years 2031 and 2033. I got sidetracked on 1 and 2 above.

Still interested in your thoughts, #Cruncher, since you're the granddaddy of TIPS ladder building tools as far as I'm concerned. Usually when you don't reply to challenges like this, you're busily working on a spreadsheet solution in the background. Fingers crossed, but if not, I'm thinking I'll get there eventually.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by kaesler »

Kevin M wrote: Tue May 28, 2024 11:03 am I have a question about both tools. Why does each one use a combination of 2034s and 2040s to cover the gap years? The #Cruncher spreadsheet uses multipliers of 3 and 4 respectively for these bracket years, and tipsladder.com uses different combinations of them depending on the options chosen for "Which TIPS to use to fund a year without a maturing TIPS:".
Speaking for tipsladder.com: at the time I could think of no other choice. For a given gap year, no existing TIPS bond matures so offer existing bonds that mature in "close" years for the varying interpretations of "close".

I've since come to understand duration matching a bit better, and was making the same assumption you were, i.e.:
Kevin M wrote: Tue May 28, 2024 11:03 am I've always assumed that this just made sense based on some sort of duration matching scheme, ...
Kevin M wrote: Tue May 28, 2024 11:03 am After thinking about it, it seems that currently we could more effectively cover the 2035 gap year with a Jan 2025 TIPS, for example, since there is more certainty of the nominal return when the 2035 is issued in Jan 2025, and the yield is much higher than the 2034 or 2040 TIPS.
I know your thinking is evolving on this, but remember that the tipsladder.com ladder generator only uses TIPS available today on the secondary market. The assumption is that the user is building a ladder today, and buying it very soon after. So the possible benefits of a bond to be auctioned next year cannot be cosiderered.

The next version of the generator will allow existing bonds, bought at auction to be integrated into a newly generated ladder.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

kaesler wrote: Fri Jun 07, 2024 7:48 am
Kevin M wrote: Tue May 28, 2024 11:03 am After thinking about it, it seems that currently we could more effectively cover the 2035 gap year with a Jan 2025 TIPS, for example, since there is more certainty of the nominal return when the 2035 is issued in Jan 2025, and the yield is much higher than the 2034 or 2040 TIPS.
I know your thinking is evolving on this, but remember that the tipsladder.com ladder generator only uses TIPS available today on the secondary market. The assumption is that the user is building a ladder today, and buying it very soon after. So the possible benefits of a bond to be auctioned next year cannot be cosiderered.
I don't understand this. I was just describing a different gap year coverage method, which would be to double up on the 2025-2029, all available now, to cover 2035-2039, then use the proceeds as the former mature to buy the latter.

But yeah, my thinking has evolved since that thought, and I'm now back to the default 4/3 or 3/4 multiplies for 2034/2040 that the tools offer as close to optimal, but with 3.5/3.5 probably being closer to optimal.

Again, my figure of merit is how close ARA/DARA is to 1 after each swap of ladder TIPS for gap year TIPS. Perhaps considering the average and standard deviation as actual measures.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by kaesler »

Kevin M wrote: Fri Jun 07, 2024 8:22 am I don't understand this. I was just describing a different gap year coverage method, which would be to double up on the 2025-2029, all available now, to cover 2035-2039, then use the proceeds as the former mature to buy the latter.
Apologies. I hadn't followed the thread closely enough to understand your proposed new coverage method.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by #Cruncher »

Kevin M wrote: Thu Jun 06, 2024 10:36 am
Kevin M wrote: Tue May 28, 2024 11:03 amI have a question about both tools.
The title of this old 2012 thread is confusing. The "Two in Particular" referred to my TIPS Ladder Builder Excel workbook and a simpler spreadsheet by Magellan. But the latter one never got much attention. And Magellan's profile indicates he hasn't posted in over two years. However, since kaesler is following your posts in this thread, I guess it's OK to use for issues that apply to both my Excel workbook and his tipsladder.com tool.
Kevin M, continuing in same post, wrote: Why does each one use a combination of 2034s and 2040s to cover the gap years? ... I've always assumed that this just made sense based on some sort of duration matching scheme, but in my thread, Filling the TIPS gap years with bracket year duration matching - Bogleheads.org, we've discovered that duration matching doesn't really work ...
In picking "3" and "4" as the default multipliers for the 2034 and 2040 maturities I just intend them to somehow cover the gap years 2035-2039. I assume "duration matching" in only a general sense. And I have to admit, Kevin, that I've only skimmed your other thread. It's gone too far into the weeds -- even for me. :wink:

Still interested in your thoughts, #Cruncher, ... Usually when you don't reply to challenges like this, you're busily working on a spreadsheet solution in the background.
I apologize for not responding to your first post, Kevin. I wasn't "busily working on a spreadsheet solution". I've just been lazy. :( However, I just now whipped together a little spreadsheet that may be of interest. It shows what happens under the following scenario:
  • Do not replace any of the 2034's or 2040's with new 10-year TIPS as they become available 2025-2039.
  • Instead hold all of them until the 2034's mature.
  • At that time sell all of the excess 2040's.
  • Use the combined proceeds (in excess of 2034's spending) to buy 1-5 year TIPS maturing in 2035-2039.
I've made the following simplifying assumptions to more easily illustrate what would happen for three different yields (-2%, 0%, and +2%) at the time the earlier TIPS mature.
  • Assume it's one year from now and the gap is only the four years 2036-2039.
  • All bonds maturing 2035-2040 are zero-coupon bonds.
  • One wants $10,000 of principal to be collected each of the gap years.
  • So one buys $20,000 extra each of the 2035 and 2040 maturities to cover these four gap years.
  • In 2035 yields will be the same for every maturity 2036-2040.

Code: Select all

Row          Col A    Col B    Col C    Col D   Formula in Col B Copied Right
  2  Annual desire   10,000
  3  Extra matures     2035     2040
  4   Amount extra   20,000   20,000
  5          Yield      -2%       0%      +2%
  6      2040 sale   22,126   20,000   18,115  =$C4/(1+B5)^($C3-$B3)
  7   Avail to buy   42,126   40,000   38,115  =$B4+B6
  8        Matures   --- Cost of Purchase ---
  9           2036  -10,204  -10,000   -9,804  =-$B$2/(1+B$5)^($A9-$B$3)
 10           2037  -10,412  -10,000   -9,612   | | |
 11           2038  -10,625  -10,000   -9,423   v v v
 12           2039  -10,842  -10,000   -9,238  =-$B$2/(1+B$5)^($A12-$B$3)
 13      Remainder       43        0       37  =B7+SUM(B9:B12)
As shown on row 13, for any of the three possible yields -- as long as the yield curve is flat for 2036-2040 -- the extra 2035's redemption plus the early sale of the extra 2040's are enough to purchase $10,000 for each of the four years 2036-2039.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

#Cruncher wrote: Fri Jun 07, 2024 2:35 pm
Kevin M wrote: Thu Jun 06, 2024 10:36 am
Kevin M wrote: Tue May 28, 2024 11:03 amI have a question about both tools.
The title of this old 2012 thread is confusing. The "Two in Particular" referred to my TIPS Ladder Builder Excel workbook and a simpler spreadsheet by Magellan. But the latter one never got much attention. And Magellan's profile indicates he hasn't posted in over two years. However, since kaesler is following your posts in this thread, I guess it's OK to use for issues that apply to both my Excel workbook and his tipsladder.com tool.
Thanks for clarifying this. I guess I hadn't read the OP in awhile, so I just assumed the second "spreasheet" was tipsladder.com; but I was wondering why you referred to it as a spreadsheet.
:oops:

I don't recall ever even looking at Magellan's spreadsheet, but since you clarified this, I downloaded it and took a quick look. I like the simplicity of it, but since it only uses the real CMT rates it's just an approximation, as you point out in the OP. It got me thinking, though, that it might be a better starting point if I ever wanted to build my own TIPS ladder spreadsheet, so that I could tweak it more to my liking, e.g., to help with analyses like I'm doing with the gap year coverage methods.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

#Cruncher wrote: Fri Jun 07, 2024 2:35 pm I apologize for not responding to your first post, Kevin. I wasn't "busily working on a spreadsheet solution". I've just been lazy. :( However, I just now whipped together a little spreadsheet that may be of interest. It shows what happens under the following scenario:
  • Do not replace any of the 2034's or 2040's with new 10-year TIPS as they become available 2025-2039.
  • Instead hold all of them until the 2034's mature.
  • At that time sell all of the excess 2040's.
  • Use the combined proceeds (in excess of 2034's spending) to buy 1-5 year TIPS maturing in 2035-2039.
I've made the following simplifying assumptions to more easily illustrate what would happen for three different yields (-2%, 0%, and +2%) at the time the earlier TIPS mature.
  • Assume it's one year from now and the gap is only the four years 2036-2039.
  • All bonds maturing 2035-2040 are zero-coupon bonds.
  • One wants $10,000 of principal to be collected each of the gap years.
  • So one buys $20,000 extra each of the 2035 and 2040 maturities to cover these four gap years.
  • In 2035 yields will be the same for every maturity 2036-2040.

Code: Select all

Row          Col A    Col B    Col C    Col D   Formula in Col B Copied Right
  2  Annual desire   10,000
  3  Extra matures     2035     2040
  4   Amount extra   20,000   20,000
  5          Yield      -2%       0%      +2%
  6      2040 sale   22,126   20,000   18,115  =$C4/(1+B5)^($C3-$B3)
  7   Avail to buy   42,126   40,000   38,115  =$B4+B6
  8        Matures   --- Cost of Purchase ---
  9           2036  -10,204  -10,000   -9,804  =-$B$2/(1+B$5)^($A9-$B$3)
 10           2037  -10,412  -10,000   -9,612   | | |
 11           2038  -10,625  -10,000   -9,423   v v v
 12           2039  -10,842  -10,000   -9,238  =-$B$2/(1+B$5)^($A12-$B$3)
 13      Remainder       43        0       37  =B7+SUM(B9:B12)
As shown on row 13, for any of the three possible yields -- as long as the yield curve is flat for 2036-2040 -- the extra 2035's redemption plus the early sale of the extra 2040's are enough to purchase $10,000 for each of the four years 2036-2039.
This is a nice, simple model. It shows basically the same thing as my somewhat more complicated model if we assume that price changes for the gap year TIPS, as it would if they were trading on the secondary market. If I'm understanding your model correctly, it makes the same assumption. You're making the additional assumption that the gap year TIPS are zero coupon, so the price/cost/value changes based on changes in yield, and in your case we can use the simplified price/cost/value formula that applies to zeros.

Where I am now in this investigation is trying to show that we derive the same financial benefit if price is fixed, which is a good first approximation for auctions, and the coupon is the dependent variable in the present value bond pricing formula. My intuition is that this is so, but I haven't wrapped it all up in a pretty package with the math demonstrating it convincingly.
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by #Cruncher »

I thought it might be good to step back and see the underlying method of building a hypothetical ladder without the complications of a real-world TIPS ladder where ...
  • In many years more than one TIPS matures.
  • But none at all currently mature 2035-2039.
  • They are only sold in $1,000 face value increments.
  • In the year of maturity some have one six-month interest payment and some have two.
In this hypothetical ladder ...
  • Exactly one TIPS matures each of the next 30 years.
  • They can be purchased in any fractional amount.
  • They have only one interest payment each year on the anniversary of their maturity date.
  • Accrued and partial year interest is ignored.
The following table shows how, working backward from year 30, we build this hypothetical ladder to produce 30,000 constant dollars each year. Each year it deducts from the 30K total required, the interest on bonds maturing in later years. (E.g., in year 30 there will be no such bonds; in year 29 there will be the interest from the bond maturing in year 30; and in year 1 there will be the interest from all the bonds maturing in years 2-30.) This balance must be met by the principal and final year interest of the TIPS maturing that year. These calculations are shown in columns C:F below.

Code: Select all

Row Col A   Col B    Col C     Col D    Col E     Col F      Col G    Col H       Selected Formulas [*]
  2  Desire Amt/Yr  30,000
  
  3                Intrest                                    YTM       YTM
  4                  Older    Needed   Annual     Total     0.000%   2.000%
  5  Year  Coupon    Bonds  Princpal  Intrest  Proceeds       Cost     Cost

Code: Select all

  6    30  2.125%        0    29,376      624    30,000     48,103   30,198   H6: =-PV(H$4,$A6,$E6,$D6,0)
  7    29  1.500%      624    28,942      434    30,000     41,531   25,781   C7: =SUM(E$6:E6)
  8    28  0.125%    1,058    28,906       36    30,000     29,917   17,372       | | |
  9    27  0.125%    1,094    28,869       36    30,000     29,844   17,661       | | |
 10    26  0.250%    1,131    28,797       72    30,000     30,669   18,657       | | |
 11    25  1.000%    1,203    28,512      285    30,000     35,640   22,946       v v v
 12    24  1.000%    1,488    28,230      282    30,000     35,005   22,891  C12: =SUM(E$6:E11)
 
 13    23  0.875%    1,770    27,985      245    30,000     33,617   22,226  D13: =(C$2-C13)/(1+B13)
 14    22  1.000%    2,015    27,708      277    30,000     33,804   22,815       | | |
 15    21  0.750%    2,292    27,502      206    30,000     31,833   21,654       | | |
 16    20  1.375%    2,498    27,129      373    30,000     34,589   24,356       | | |
 17    19  0.625%    2,871    26,960      169    30,000     30,162   21,148       v v v
 18    18  0.750%    3,040    26,760      201    30,000     30,372   21,745  D18: =(C$2-C18)/(1+B18)
 
 19    17  2.125%    3,240    26,203      557    30,000     35,669   26,671  E19: =D19*B19
 20    16  2.125%    3,797    25,658      545    30,000     34,381   26,093       | | |
 21    15  1.000%    4,342    25,404      254    30,000     29,214   22,139       | | |
 22    14  1.000%    4,596    25,152      252    30,000     28,673   22,107       | | |
 23    13  1.000%    4,848    24,903      249    30,000     28,140   22,077       v v v
 24    12  1.000%    5,097    24,656      247    30,000     27,615   22,049  E24: =D24*B24
 
 25    11  1.000%    5,344    24,412      244    30,000     27,098   22,023  F25: =SUM(C25:E25)
 26    10  1.750%    5,588    23,992      420    30,000     28,191   23,454       | | |
 27     9  1.125%    6,008    23,725      267    30,000     26,128   22,031       | | |
 28     8  0.125%    6,275    23,696       30    30,000     23,933   20,441       | | |
 29     7  0.125%    6,304    23,666       30    30,000     23,873   20,794       v v v
 30     6  0.125%    6,334    23,637       30    30,000     23,814   21,154  F30: =SUM(C30:E30)
 
 31     5  2.125%    6,363    23,145      492    30,000     25,604   23,281  G31: =-PV(G$4,$A31,$E31,$D31,0)
 32     4  1.250%    6,855    22,859      286    30,000     24,002   22,206       | | |
 33     3  0.125%    7,141    22,831       29    30,000     22,916   21,596       | | |
 34     2  0.125%    7,169    22,802       29    30,000     22,859   21,972       v v v
 35     1  0.125%    7,198    22,774       28    30,000     22,802   22,355  G35: =-PV(G$4,$A35,$E35,$D35,0)

Code: Select all

 36   Sum          117,583   775,190    7,226   900,000    900,000  671,894  C36: =SUM(C6:C35)
I've added columns G and H to calculate the cost of each bond assuming either a 0% or 2% yield-to-maturity (YTM). Note how the cost is higher for bonds with larger coupons and more time until maturity. The total costs are shown in cells G36 and H36. Because of the simplifying assumptions and since I'm assuming the same YTM for all bonds, these totals could also be quickly calculated with the PV function:

900,000 = -PV(0%, 30, 30000, 0, 0)
671,894 = -PV(2%, 30, 30000, 0, 0)
or, without the use of a function:
900,000 = 30000 * 30
671,894 = 30000 * (1 - 1 / 1.02 ^ 30) / 0.02

* The formulas in cell C7 and in cells D6:H6 are copied down to row 35. The formula in cell C36 is copied right to column H.

6/13/2024: Since I see this spreadsheet referenced in another post, I thought it might be good to provide instructions for more easily duplicating it in Excel.
  • Select All, Copy, and Paste [**] the following at cell A2 of a blank Excel sheet:

    Code: Select all

    Desire Amt/Yr		30000
    	 	Intrest	 	 	 	YTM 	YTM
    	 	Older	Needed	Annual	Total	0	0.02
    Year	Coupon	Bonds	Princpal	Intrest	Proceeds	Cost	Cost
    30	0.02125	0	=(C$2-C6)/(1+B6)	=D6*B6	=SUM(C6:E6)	=-PV(G$4,$A6,$E6,$D6,0)
    =A6-1	0.015	=SUM(E$6:E6)
    =A7-1	0.00125
    =A8-1	0.00125
    =A9-1	0.0025
    =A10-1	0.01
    =A11-1	0.01
    =A12-1	0.00875
    =A13-1	0.01
    =A14-1	0.0075
    =A15-1	0.01375
    =A16-1	0.00625
    =A17-1	0.0075
    =A18-1	0.02125
    =A19-1	0.02125
    =A20-1	0.01
    =A21-1	0.01
    =A22-1	0.01
    =A23-1	0.01
    =A24-1	0.01
    =A25-1	0.0175
    =A26-1	0.01125
    =A27-1	0.00125
    =A28-1	0.00125
    =A29-1	0.00125
    =A30-1	0.02125
    =A31-1	0.0125
    =A32-1	0.00125
    =A33-1	0.00125
    =A34-1	0.00125
    Sum	 	=SUM(C6:C35)
  • Copy cell G6 right to column H.
  • Copy cells D6:H6 down one row.
  • Copy cells C7:H7 down to row 35.
  • Copy cell C36 right to column H.
  • Format for readability.
** If you have trouble pasting, try Paste Special and Text.
Last edited by #Cruncher on Thu Jun 13, 2024 5:41 am, edited 1 time in total.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

^This is fantastic! I'm pretty certain I'll take a shot at using this spreadsheet for the gap year duration matching analysis I've been doing. I've figured it out using your actual spreadsheet, but of course it's much more complicated with all of the extra rows and columns.

Thanks much.

:sharebeer
If I make a calculation error, #Cruncher probably will let me know.
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Re: TIPS Ladder Spreadsheets in General & Two in Particular

Post by Kevin M »

#Cruncher wrote: Mon Jun 10, 2024 7:28 pm 6/13/2024: Since I see this spreadsheet referenced in another post, I thought it might be good to provide instructions for more easily duplicating it in Excel.

<snip>
I thought of asking you for something like this, but I decided it would help my understanding to work it out with what you provided, and it did I think.
If I make a calculation error, #Cruncher probably will let me know.
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